It didn't take long for the NFL's new domestic violence policy to get its first test case.

Three days. That has to make Roger Goodell shudder.

In spite of the strong message the NFL commissioner delivered last week to clarify how the league won't tolerate domestic violence – a six-game suspension for a first offense, an indefinite ban for a second incident – it apparently wasn't enough of a deterrent to prevent a situation that led to another arrest of an NFL player.

Still, the new policy added to the impression Goodell is equipped to restore public trust that can swing with off-the-field issues.

He can't stop now.

Here are five more things the commissioner needs to do, now.

Strengthen the alcohol policy: Since 2000, more than a quarter of NFL player arrests (which occur at a lower rate than the general population) during that span have involved DUI cases.

It takes a second alcohol-related offense, though, to trigger a possible suspension.

This is hardly a matter that Goodell can resolve alone. The alcohol policy is part of a comprehensive drug policy that needs to be updated, which includes the debate of whether to liberalize standards for marijuana testing. And it's connected to the stalled implementation of human growth hormone testing, which is included in the steroids policy.

All of these matters have been on hold since the labor deal was struck in 2011, with the players union seeking to strip Goodell of power in disciplining players, which would include cases where there were no failed drug tests.

Goodell needs to keep the communication flowing with the union.

The agreement struck in Aldon Smith's suspension should be a template for future cases. Rather than being barred from the San Francisco 49ers facility while suspended, Smith will be allowed to attend meetings and work out at team headquarters – where he can also draw on organizational support.

Establish a code of conduct for owners: Teams entrusted Goodell to preside in the best interests of the NFL, and owners need to back him in enforcing discipline on one of their own.

Public trust doesn't merely swing with how players are disciplined.

Indianapolis Colts owner Jim Irsay reached a plea agreement on Friday for two impaired driving charges that stemmed from a March arrest. Terms of the plea deal will be revealed at a hearing on Tuesday, and with resolution of the case the spotlight will shift back on Goodell.

If the discipline on Irsay is perceived to be too light, Goodell may face similar backlash he saw after disciplining Ray Rice. Then again, suspending an owner is nothing like suspending the team's top pass-rusher for a few games.

If players are to be disciplined for issues that arise away from team headquarters, owners should be held to high standards, too, regardless of whether it involves NFL business.

Owners are vetted when they purchase franchises and potentially rejected if there are issues with their other businesses. Once they join the exclusive owner's club, the vetting shouldn't stop.

Change his stance on Washington's team name: It's one thing for Daniel Snyder to stand on the wrong side of history and defend the use of Washington's racially-insensitive name.

For Goodell to ignore opposition to the team name – which includes the urging of lawmakers and the decision of the U.S. Patent and Trademark Office, pending Snyder's appeal – sure doesn't square with the league's initiatives regarding respect in the workplace.

The NFL has taken a stance denouncing the use of the N-word and gay slurs but won't take a position to eradicate the use of a team nickname that is defined as a racial slur.

Goodell can do better than echoing Snyder's contention that by using the team name – instituted by a bigot, team founder George Preston Marshall – honors tradition.

Times have changed.

We know that Goodell can change culture. Look at what has occurred in recent years on the concussion front, in the name of safety and long-term health and in the face of litigation.

In addition to sweeping new protocols and standards in the NFL, the league's clout has helped change laws in all 50 states, governing the monitoring and treatment of high school athletes suspected of suffering head injuries.

Pursue a developmental league: When the NFL expanded the practice squads this summer, creating 64 new jobs across the league, it was a good first step. Teams need the extra bodies to get through the week of game preparation.

Even better, though, would be a developmental league that would allow hundreds of additional players to improve their skills while in the pipeline for advancement. With attrition and injuries, the additional players may be needed, eventually.

Yet more than that, it's a quality measure. A D-league would be the opportunity for quarterbacks and offensive linemen to get the game repetitions they can't get on a practice squad.

Remember, Kurt Warner once played in the NFL Europe.

Sure, the league's European developmental leagues fizzled. They don't need to go overseas again for this. And they definitely should not play in the spring.

Anybody for Wednesday Night Football?

Los Angeles, not London: As much as the NFL has worked to expand its global reach, the talk about having a permanent franchise in London is a bit much.

I'm thinking that Goodell should send a clear message the next time someone asks about that – and it's coming soon, with more regular-season games headed to the UK this season.

The pecking order begins with Los Angeles. It has been 19 years and counting without an NFL franchise in the nation's second-largest market.

London is now the Jacksonville Jaguars' second home and the NFL has added another game this fall. Let the market keep growing, with T-shirt sales to boot.